Simulation of fields around spring and cathode for photogun

1. Simulation of fields around spring and cathode for photogun D. Lipka, MDI, DESY Hamburg

2. Goal Simulate fields in gun (here gun design version 5 is used) Monitor fields at spring and cathode region to find unexpected high fields

3. Setup • Gun version 5 • Frequency domain solver around 1.3 GHz • Fields are scaled to 60 MV/m at cathode surface • Body copper

4. Present cathode region setup • Materials: • Cathode: Molybdenum • Spring: CuBe (conductivity 25∙106 S/m) or Silver • Backplane (blue): stainless steel • Blue line: on this line field strength will be monitored • Holder at backplane is simplified to increase the field resolution (more mesh cells possible)

5. Setup • 85 lamella around cathode • Contact verified on inner spring to cathode and lamella to the other • Contact of spring to copper body too

6. Mesh view Use tetrahedral mesh Large cells in resonator, very small cells at cathode region for high resolution

7. Boundary and symmetry Symmetry on yz-plane with magnetic Ht=0 Magnetic boundary at transverse coordinates Electric boundary at z=max Open boundary at z=min

8. Reflection result Each frequency domain simulation produces reflection like shown here, p-mode is at 1299.82 MHz

9. Scaled E-field • The fields are scaled such that E=60 MV/m at the cathode surface is generated, • here the absolute E-field along the z-axis is shown, • almost perfect field balance visible

10. Scaled E-field • Here monitored the E-field along the x-axis at the surface of the cathode and further • Higher field of almost 90 MV/m found at the corner of the cathode, smaller at the corner of the copper wall

11. Scaled H-field distribution • The maximum of H-field is at the rounding of the resonators, Hmax=133 kA/m • At the cathode it is much smaller, details will be given for different cases

12. Different cases Beside the default setup different cases are investigated: One missing lamella 11 missing lamella 11 shifted lamella cut sphere (no contact to (in addition to cathode) shifted lamella)

13. E-field on curve Absolute E-field along the cathode line shown; unit: V/m Default: ends at about 13.5 mm Missing lamella: slightly higher field 11 missing lamella: more field toward other end of cathode Shifted lamella and cut sphere (similar): more field behind cathode Similar for silver and CuBe

14. E-field distribution Shown for default and cut sphere case Results: no significant higher field at the additional peak for the last case

15. H-field on curve Absolute H-field along the cathode line shown; unit A/m Default: high field spike at connection to spring 1 missing lamella: field smeared out 11 missing lamella: more smearing Shifted lamella and cut sphere (similar): longer behind cathode Similar to silver and CuBe Field distributions in the following slides

16. H-field distribution default case H-field strength at cathode is smaller compared to cavity, but at the junction between spring to cathode or holder higher local fields visible

17. H-field distribution default case Here the local field spikes are visible at the cathode and spring

18. H-field distribution: missing lamella At the monitoring line the field strength is reduced but at the other contacts the field strength is slightly higher

19. H-field distribution: 11 missing lamella A larger area get a reduced field, but at the starting spring the field is higher compared to the default case

20. H-field distribution: 11 shifted lamella Like it is shown along the curve on the slide before the field strength is more smeared, but still higher field at the first contact

21. H-field maximum at cathode • Taking the maximum field strength on the cathode the surface current can be calculated with: • Surface current I=H∙2pr/√2, with r the radius • For the different cases the maximum current are: • Default: 1207 A • Missing lamella: 1268 A • 11 missing lamella: 1634 A • 11 shifted lamella: 1926 A

22. Summary Simulation of gun 5 with present cathode design and different cases E-field: at corner higher field, behind is lower H-field: strong difference between different cases, higher field and therefore higher surface current when spring does not have a good contact to cathode

23. New spring and holder design I got the new holder and spring design, see 3D model on right, Simulation: same settings

24. New spring and holder design View around spring, 45 lamellas

25. Mesh view On the right side the mesh view, low mesh sizes for cathode and spring and holder around defined

26. E-field along line E-field on right plot in V/m Similar field along z-axis, similar field on cathode surface in resonator compared to present design, a little bit longer field to the backside of cathode due to spring position is more behind, amplitude on cathode side few MV/m and lower

27. H-field along line H-field on right plot in A/m Seems to be no spike at cathode, but see next slide …

28. H-field on cathode Before the contact with spring high field: 28 kA/m (line was just between two lamellas) Corresponds to 1061 A surface current, lower than present design (1207 A) But …

29. Missing lamella Introducing a bad contact of spring, I removed 6 lamellas, see design on right

30. H-field on cathode with missing lamellas A strong H-field at the first contact on the cathode is produced with 67.6 kA, which corresponds to 2552 A surface current (higher compared to the failure setting with present design 1926 A)